Plasma density effects on atomic reaction rates

Plasma modeling and diagnostics commonly involve solution of rate equations for the population densities of impurity ions in their excited and charge states. Construction of the rate equations requires a complete set of atomic transition rates for all the charge and excited states involved. However, the rates are themselves affected by the host plasma ions and electrons. The ionic and electronic effects in a two-component plasma are intimately interconnected, especially when the rate equations are simplified for computational purpose in the determination of ionization balance. We formulate a coherent approach to the problem of the plasma density effect, and apply it to carbon impurities in a hydrogen plasma. Both the plasma field distortion of atomic states and the corresponding rates by the plasma ions and stochastic plasma collisional transitions caused by the plasma electrons are included. The latter effect is estimated by constructing an effective collisional transition operator, and the electron-ion recombination processes are explicitly evaluated. It is shown that, these two effects of the ionic field distortions and electronic collisions tend to cancel each other, resulting in many cases in reducing the overall effect of the plasma density on the ionization.